Solving the heat equation symbolically with MuSimp
type: Item
instance of: scholarly article
title: Solving the heat equation symbolically with MuSimp
zbMATH Open document ID: 0671.35032
DOI: 10.1016/S0747-7171(88)80037-3
published in: Journal of Symbolic Computation
publication date: 1988-01-01T00:00:00Z
review text: We derive an algorithm suitable for a small computer algebra system (MuSimp) which solves the heat equation given inital values \(u(x,t_ 0)=\phi (x)\), where \(\phi\) is a polynomial, without having to evaluate the heat integral. Uniqueness of the solutions follows from the fact that polynomial solutions of the heat equation have Huygens' property. We also derive an algorithm for the boundary value (finite bar) problem. We first discuss the case of one space dimension.
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 4097899
zbMATH Keywords: algorithm
zbMATH Keywords: computer algebra
zbMATH Keywords: heat equation
zbMATH Keywords: inital values
zbMATH Keywords: Uniqueness of the solutions
zbMATH Keywords: polynomial solutions
zbMATH Keywords: Huygens' property
author: C. P. Mawata
MaRDI profile type: Publication
cites work: Q5785591
cites work: Expansions in Terms of Heat Polynomials and Associated Functions
cites work: Q4084640
full work available at URL: s0747-7171(88)80037-3
OpenAlex ID: W2071134945
description: scientific article; zbMATH DE number 4097899